Put the potatoes in a medium saucepan and cover with hot water. Cook over high heat until tender, about 12 minutes.

Meanwhile, heat the oil in a large, heavy casserole. Add the chicken and cook over high heat until lightly browned, 4 minutes. Add the onion and jalapeño and cook, stirring, until the onion is softened, 4 minutes. Add 3 tablespoons of the fish sauce and the stock and bring to a boil. Cover and cook over moderate heat until the chicken is just cooked through, about 10 minutes.

Using a slotted spoon, transfer the potatoes to a ricer and press into a bowl. (Alternatively, mash the potatoes.) Reserve the potato water. Add the 2 tablespoons of flour, egg yolk, chives and 1/2 teaspoon of salt to the potatoes and stir until a stiff dough forms. Turn the dough out onto a heavily floured board and divide it in half. Roll each piece into a 1/2-inch-thick rope. Cut the ropes into 1-inch pieces.

Add the bok choy to the stew and cook until crisp-tender, about 5 minutes. Add the cornstarch mixture and cook, stirring, until thickened, 1 minute.

Return the potato water to a boil and add the dumplings. Cook over high heat until they rise to the surface, then simmer for 2 minutes. Using a slotted spoon, transfer to the chicken stew. Add the basil and the remaining 1 tablespoon of fish sauce and simmer the stew for 2 to 3 minutes. Serve with lime wedges.